A probe into the fatigue crack growth in mechanical systems with hyperchaotic/chaotic dynamics

Abstract

This study presents experimental and analytical fatigue frameworks for the dynamic fatigue life prediction of nonlinear mechanical systems under hyperchaotic oscillations. Fatigue in aluminium notched beams under hyperchaotic/chaotic vibrations is studied using a time-based analytical model. The fatigue lives obtained by the analytical model provided satisfactory correlations with those acquired by the dynamic fatigue experiments conducted on cracked aluminium beams. The model is then used to study the fatigue under Duffing chaotic, Duffing hyperchaotic, and periodic dynamic forcing. Results indicate that the classic linear cumulative damage rule delivers inaccurate high cycle fatigue (HCF) predictions under chaotic and hyperchaotic loading. Proper prediction of the HCF in metallic mechanical components experiencing chaotic and hyperchaotic dynamics requires time-based fracture-mechanics analytical models, such as that proposed in the current study. Under similar elastic energy inputs, hyperchaotic loading brings higher fatigue damage than chaotic and periodic loading. The fatigue life sensitivity to initial conditions is high under hyperchaotic, moderate under chaotic and next-zero under periodic loading.